Question

Charlotte is going to flip 3 quarters and lists the sample space in a tree diagram.



How many outcomes are possible from flipping 3 quarters?

(1 point)
Responses

12
1 half

4
4

8
8

64
64
Question 2
What is the probability that all 3 quarters will land on tails?(1 point)
Responses

2
2

1
1

14
1 fourth

18

Answer 1

To determine how many outcomes are possible from flipping 3 quarters, we can analyze the situation as follows:

Each quarter can land in one of two ways: heads (H) or tails (T). Therefore, when flipping 3 quarters, each quarter has 2 outcomes.

The total number of outcomes can be calculated by using the formula for the total outcomes \( n = 2^k \), where \( k \) is the number of coins being flipped.

So, for 3 quarters:
\[
n = 2^3 = 8
\]

Thus, there are 8 possible outcomes when flipping 3 quarters.

Now, let's look at the second question regarding the probability that all 3 quarters will land on tails.

The only outcome in which all 3 quarters land on tails is TTT. To find the probability of this event, we can use the formula for probability:

\[
P(\text{all tails}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}
\]

In our case, there is 1 favorable outcome (TTT) and 8 total outcomes.

So the probability is:
\[
P(\text{all tails}) = \frac{1}{8}
\]

To summarize:

1. The total number of outcomes from flipping 3 quarters is **8**.
2. The probability that all 3 quarters will land on tails is **\(\frac{1}{8}\)**.

If the provided answer options are correct, the appropriate choices would be:
- **8** for the number of outcomes.
- **\(\frac{1}{8}\)** for the probability (considering options may vary).